Complements of Mathematics 1
A.Y. 2022/2023
Learning objectives
Present a wide range of classical algebra issues by building basic knowledge in elementary algebra from a higher point of view.
Expected learning outcomes
Application of knowledge and methods for the solution of classical algebra problems.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
The course will focus on the concept of number. Natural numbers, prime numbers and zero. Algebraic and transcendent numbers, Diophantine equations and roots. Fields and splitting fields. Construction with ruler and compass. Elements of Galois theory.
Real and complex numbers. Formally real fields, Archimedean and non-Archimedean. Algebraic, real and Archimedean closures. Complete fields and uniqueness of the field of real numbers. Quaternions. Integers of Hurwitz.
Real and complex numbers. Formally real fields, Archimedean and non-Archimedean. Algebraic, real and Archimedean closures. Complete fields and uniqueness of the field of real numbers. Quaternions. Integers of Hurwitz.
Prerequisites for admission
Knowledge of the common basic notions (mainly of algebra) covered in the programs of the first and second year courses of mathematics is required.
Teaching methods
Lectures
Teaching Resources
Algebra, M. Artin: Bollati Boringhieri, 1997. Ultima edizione (in inglese): Algebra (2nd Edition) Addison Wesley, 2010
Teoria dei campi, Mario Girardi e Giorgio Israel: Feltrinelli, 1976
C'era una volta un numero, G.G. Joseph: La vera storia della matematica. Il Saggiatore, 2000.
Teoria dei campi, Mario Girardi e Giorgio Israel: Feltrinelli, 1976
C'era una volta un numero, G.G. Joseph: La vera storia della matematica. Il Saggiatore, 2000.
Assessment methods and Criteria
Oral exam on the topics of the course. Students are invited to agree on a topic for conducting a seminar.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Lessons: 42 hours
Professors:
Barbieri Viale Luca, Venerucci Rodolfo
Educational website(s)
Professor(s)
Reception:
Email contact (usually for Tuesday h. 2-4 p.m.)
Office - Math Department